Principles of Managerial
Finance
9th Edition
Chapter 9
Capital Budgeting
Techniques
Learning Objectives
• Understand the role of capital budgeting techniques in
the capital budgeting process.
• Calculate, interpret, and evaluate the payback period.
• Calculate, interpret, and evaluate the net present
value (NPV).
• Calculate, interpret, and evaluate the internal rate of
return (IRR).
Learning Objectives
• Use the net present value profiles to compare net
present value and internal rate of return techniques.
• Discuss NPV and IRR in terms of conflicting rankings
and the theoretical and practical strengths of each
approach.
Techniques that Ignore the
Time Value of Money
• Payback. The payback method simply measures how
long (in years and/or months) it takes to recover the
initial investment.
• But payback has two major weaknesses:
• First, it fails to consider the importance of the time
value of money.
• Second, it fails to consider cash flows that occur after
the pre-set payback period.
Techniques that Ignore the
Time Value of Money
• Payback Weakness: Failure to consider the
time value of money (pattern of cash flows).
Mactool Payback Example
(Failure to Recognize TVM)
But which is
preferred?
Payback is the
same!
Cash Flow
Project 1
Project 2
Initial Outlay
45000
45000
Year 1 Inflow
20000
25000
Year 2 Inflow
25000
20000
2 years
2 years
Payback
Techniques that Ignore the
Time Value of Money
• Payback Weakness: Failure to consider all
relevant cash flows.
Mactool Payback Example
(Failure to Recognize ALL Cash Flows)
But look at the
total cash flows
for Project 1!
Payback says
pick Project 2!
Cash Flow
Project 1
Project 2
Initial Outlay
45000
45000
Year 1 Inflow
20000
25000
Year 2 Inflow
20000
20000
Year 3 Inflow
25000
15000
Year 4 Inflow
30000
10000
Year 5 Inflow
35000
5000
2.2 years
2 years
Payback
Time Value Techniques
• Net Present Value (NPV). Net Present Value is found
by subtracting the present value of the after-tax
outflows from the present value of the after-tax
inflows.
Decision Criteria
If NPV > 0, accept the project
If NPV < 0, reject the project
If NPV = 0, indifferent
Time Value Techniques
Net Present Value
Recall the Net Incremental Cash Flows for East
Coast Drydock from Chapter 8
East Coast Drydock
Net Incremental After Tax Cash Flows
Year
0
Existing
$
-
Hoist A
$
(37,488) $
Hoist B
(51,488)
1
9,936
6,504
8,064
2
9,936
8,808
12,144
3
9,040
7,208
11,120
4
8,400
6,504
10,080
5
8,400
19,264
29,880
Time Value Techniques
Net Present Value
With a 15% discount rate, we would keep
the existing hoist
East Coast Drydock
Net Incremental After Tax Cash Flows
(NPV @ 15%)
1
(1  0.15) i
Year
PVIF
0
1.0000
1
Existing PV Existing
$
Hoist A
PV Hoist A
Hoist B
PV Hoist B
-
$
-
$ (37,488) $
0.8696
9,936
$
8,640
6,504
$
5,656
8,064
$
7,012
2
0.7561
9,936
$
7,513
8,808
$
6,660
12,144
$
9,183
3
0.6575
9,040
$
5,944
7,208
$
4,739
11,120
$
7,312
4
0.5718
8,400
$
4,803
6,504
$
3,719
10,080
$
5,763
5
0.4972
8,400
$
4,176
19,264
$
9,578
29,880
$
14,856
$
31,076
$
(7,137)
$
(7,363)
NPV = Sum of PV of CF
(37,488) $ (51,488) $ (51,488)
Time Value Techniques
Net Present Value
In fact, even with a discount rate of 0%, we would keep
the existing hoist since it has the highest NPV.
East Coast Drydock
Net Incremental After Tax Cash Flows
(NPV @ 0%)
Year
PVIF
0
1.0000
1
Existing PV Existing
$
Hoist A
PV Hoist A
Hoist B
PV Hoist B
-
$
-
$ (37,488) $
1.0000
9,936
$
9,936
6,504
$
6,504
8,064
$
8,064
2
1.0000
9,936
$
9,936
8,808
$
8,808
12,144
$
12,144
3
1.0000
9,040
$
9,040
7,208
$
7,208
11,120
$
11,120
4
1.0000
8,400
$
8,400
6,504
$
6,504
10,080
$
10,080
5
1.0000
8,400
$
8,400
19,264
$
19,264
29,880
$
29,880
$
45,712
$
10,800
$
19,800
NPV = Sum of PV of CF
(37,488) $ (51,488) $ (51,488)
Time Value Techniques
Net Present Value
Recall that the before tax operating cash inflows for
Drydock in Chapter 9 were as follows:
East Coast Drydock
Profits Before Depreciation & Taxes
Year
1
Hoist A
$
21,000
Hoist B
$
22,000
Existing
$
14,000
2
21,000
24,000
14,000
3
21,000
26,000
14,000
4
21,000
26,000
14,000
5
21,000
26,000
14,000
Time Value Techniques
Net Present Value
What if -- because of a measurement error -- the cash
inflows for A and B were double those initially
estimated as shown below:
East Coast Drydock
Profits Before Depreciation & Taxes
Year
1
Hoist A
$
42,000
Hoist B
$
44,000
Existing
$
14,000
2
42,000
48,000
14,000
3
42,000
52,000
14,000
4
42,000
52,000
14,000
5
42,000
52,000
14,000
Time Value Techniques
Net Present Value
Recalculating the NPV at a discount rate of
15%, we get:
此資料由第
一期計算，
財務計算機
則由第零期
計算
East Coast Drydock
Net Incremental After Tax Cash Flows
(NPV @ 15%)
Year
PVIF
0
1.0000
1
Existing PV Existing
$
-
$
-
0.8696
9,936
$
8,640
2
0.7561
9,936
$
7,513
3
0.6575
9,040
$
5,944
4
0.5718
8,400
$
4,803
5
0.4972
8,400
$
4,176
$
31,076
NPV = Sum of PV of CF
Hoist A
PV Hoist A
$ (37,488) $
Hoist B
PV Hoist B
(37,488) $ (51,488) $ (51,488)
19,104
$
16,612
21,264
The
Excel
function
for $
21,408 $
16,188
$
computing
NPV26,544
is
19,808 $
13,024
26,720 $
=NPV(int
rate,
data
range)
19,104 $
10,923
25,680 $
31,864
$
15,842
$
35,101
45,480
18,490
20,071
17,569
14,683
$
22,612
$
41,937
Time Value Techniques
Net Present Value
With the new numbers, we can now see that
Hoist B should be used to replace the
existing hoist. This will maximize NPV and
ultimately, shareholder value.
Time Value Techniques
Internal Rate of Return
• The IRR is the discount rate that will equate the
present value of the outflows with the present
value of the inflows:
• The IRR is the project’s intrinsic rate of return.
Decision Criteria
If IRR > k, accept the project
If IRR < k, reject the project
If IRR = k, indifferent
Time Value Techniques
Internal Rate of Return
Note that both replacement projects provide a
return in excess of the cost of capital of 15%.
East Coast Drydock
Net Incremental After Tax Cash Flows
IRR on Excel
無法計算
其IRR
Year
PVIF
0
1.0000
1
Existing PV Existing
$
PV Hoist A
-
$
0.7033
9,936
$
2
0.4946
9,936
$
3
0.3479
9,040
$
4
0.2447
8,400
$
2,055
19,104
$
5
0.1721
8,400
$
1,445
31,864
$
Internal Rate of Return
-
Hoist A
$ (37,488) $
Hoist B
PV Hoist B
(37,488) $ (51,488) $ (51,488)
The
Excel19,104
function
for
6,988
$
13,436
4,915
21,408 IRR
$ is
10,589
computing
3,145
19,808range)
$
6,891
=IRR(data
47.63%
此資料由第零期計算，
財務計算機也由第零期
計算
21,264
$
14,955
26,544
$
13,129
26,720
$
9,295
4,674
25,680
$
6,283
5,483
45,480
$
7,826
42.19%
Time Value Techniques
Internal Rate of Return
What if the cost of capital were 42.19%?
East Coast Drydock
Net Incremental After Tax Cash Flows
(NPV @ 42.19%)
Year
PVIF
0
1.0000
1
Existing
$
PV Existing
Hoist A
PV Hoist A
-
$
-
$ (37,488) $
(37,488)
0.7033
9,936
$
6,988
19,104
$
13,436
2
0.4946
9,936
$
4,915
21,408
$
10,589
3
0.3479
9,040
$
3,145
19,808
$
6,891
4
0.2447
8,400
$
2,055
19,104
$
4,674
5
0.1721
8,400
$
1,445
31,864
$
5,483
Internal Rate of Return
Net Present Value
Profitability Index
47.63%
$
18,548
Notice that
Hoist for
B Hoist
PV Hoist
B,B
$ (51,488)
IRR$ =(51,488)
the
21,264discount
$ 14,955
26,544 $ 13,129
rate and that
26,720 $
9,295
NPV = 0
25,680
$
6,283
45,480
$
7,826
42.19%
$
3,584
1.10
$
(0)
1.00
IRR的應用
• 元智大學提供教職員優惠的年金保險，參加人員每年
將依個人服務年資由學校補助一萬五仟元（服務十年
以上）、一萬元（服務六至九年）及伍仟元（服務五
年以下）。根據該保險經紀人公司的試算結果，去計
算該項年金保險的內部報酬率：
假設現年三十九歲女性教職員，本校服務年資兩年，
首欄的數字為連續十年繳納年金保險費(扣除掉5%的
單利以及學校提撥的金額)，於第十八年時全數領出；
次欄的數字為連續十年繳納年金保險費(扣除掉5%的
單利以及學校提撥的金額)，於第十九年時全數領
出。兩者用EXCEL計算出來的內部報酬率(IRR)都是
6%，遠高於現行市場上任何的定存利率。
Time Value Techniques
Net Present Value Profile
The NPV Profile shows how a project’s value
changes with changes in the discount rate.
NPV Profile
Discount
NPV @ Various Discount Rates
Rate
Existing
Hoist A
Hoist B
0%
$
45,712
$
73,800
$
94,200
5%
$
39,777
$
57,918
$
72,683
10%
$
34,989
$
45,287
$
55,635
15%
$
31,076
$
35,101
$
41,937
20%
$
27,838
$
26,780
$
30,790
30%
$
22,841
$
14,162
$
13,978
40%
$
19,209
$
5,196
$
2,122
50%
$
16,484
$
(1,399) $
(6,536)
Time Value Techniques
Net Present Value Profile
East Coast Drydock Net Present Value Profile
NPV ($)
Existing
Hoist A
Hoist B
$100,000
$80,000
只有當K大於
這點時，NPV
與IRR的決策
是一致的
$60,000
$40,000
$20,000
47.63%
$0
0%
5%
10%
15%
20%
30%
40%
42.19%
($20,000)
k (%)
50%
Time Value Techniques
Profitability Index
• The profitability index which is also
sometimes called the benefit/cost ratio, is the
ratio of the present value of the inflows to the
present value of the outflows.
PI =
PV Inflows
PV Outflows
Decision Criteria
If PI > 1, accept the project
If PI < 1, reject the project
If PI = 1, indifferent
Time Value Techniques
Double A和B的
cash flow後
Profitability Index
Returning to the last East Coast Drydock example, we get:
East Coast Drydock
Net Incremental After Tax Cash Flows
(NPV @ 15%)
Year
PVIF
0
1.0000
1
Existing
$
PV Existing
Hoist A
PV Hoist A
Hoist B
PV Hoist B
-
$
-
$ (37,488) $
0.8696
9,936
$
8,640
19,104
$
16,612
21,264
$
18,490
2
0.7561
9,936
$
7,513
21,408
$
16,188
26,544
$
20,071
3
0.6575
9,040
$
5,944
19,808
$
13,024
26,720
$
17,569
4
0.5718
8,400
$
4,803
19,104
$
10,923
25,680
$
14,683
5
0.4972
8,400
$
4,176
31,864
$
15,842
45,480
$
22,612
Profitability Index
(37,488) $ (51,488) $
1.94
Choose Hoist A since PIA > PIB
(51,488)
1.81
Problems with Discounted Cash Flow
Techniques
Conflicting Rankings for Mutually Exclusive Projects
Mutually exclusive projects compete in some way with the
same resources. A firm can pick one, or the other, but not
both.
Dyer, Inc., Project Analysis
(Mutually Exclusive Projects)
Project
Year
A
B
Acquisition Cost
0
(100,000)
(60,000)
Cash Inflow s
1
60,000
36,000
2
60,000
36,000
3
60,000
36,000
$39,300.00
$23,580.00
NPV (@14%)
IRR
36%
36%
Problems with Discounted Cash Flow
Techniques
Conflicting Rankings for Mutually Exclusive Projects
Mutually exclusive projects compete in some way with the
same resources. A firm can pick one, or the other, but not
both.
Dyer, Inc
NPV Profile
Proje ct
rate
NPV(A)
NPV(B)
0%
$
80,000
$
48,000
10%
$
49,211
$
29,527
20%
$
26,389
$
15,833
30%
$
8,967
$
5,380
40%
$
(4,665)
$
(2,799)
50%
$ (15,556)
$
(9,333)
NPV
Problems with Discounted Cash Flow
Techniques
Conflicting Rankings for Mutually Exclusive Projects
If k<e
If e<k<f
If k>f
e f g A
$100,000B
NPV Profile
(Mutually Exclusive Projects)
兩個project的IRR皆為36%
亦即NPV=0時的K皆為36%
k(%)
Project A
$80,000
Project B
若AB為mutually exclusive，則當k<36%時，選A
當k>36%時，都不要
若AB為Independent，當k<36%，2者都選
當k>36%，都不要
$60,000
$40,000
$20,000
36%
$$(20,000)
$(40,000)
0%
10%
20%
30%
40%
50%
60%
Problems with Discounted Cash Flow
Techniques
Conflicting Rankings for Mutually Exclusive Projects
• Interdependent projects are those that
influence the value of others.
• In general terms, if there are two
interdependent projects, then three appraisals
are required:
– Project A
如：兩家鄰近的購物中心
– Project B
– And Project A plus B
Problems with Discounted Cash Flow
Techniques
Summary
• If projects are mutually exclusive and not subject
to capital rationing, the project with the higher NPV
should be selected.
• If the projects are independent, and there is no
capital restriction, both should be chosen if they
have positive NPVs.
• In the presence of capital restrictions, the project
with the higher NPV should be selected.
Table 9.7 Reinvestment Rate Comparisons for a Projecta
Reinvestment rate
Number of
10%
years earning
Cash
interest (t)
Future value
Year
inflows
[3-(1)]
FVIF10%,t [(2)×(4)]
(1)
(2)
(3)
(4)
(5)
1
$52,000
2
1.210
$62,920
2
78,000
1
1.100
$85,800
3
100,000
0
1.000
$100,000
Future Value end of year 3
$248,720
NPV @ 10%=$16,867 > 0 ∴accept
IRR=15% > 10% ∴accept
a
15%
FVIF15%,t
(6)
1.323
1.150
1.000
Future Value
[(2)×(6)]
(7)
$68,796
$89,700
$100,000
$258,496
Initial investment in this project is $170,000.
-170,000 +52,000 +78,000 +100,000
0
1
2
3
52,000 78,000 100,000


 16,867
(1.1)1
(1.1) 2
(1.1)3
52,000 78,000 100,000
IRR : 170,000 


 r  15%
(1  r )1 (1  r ) 2 (1  r )3
NPV  170,000 
Table 9.8
Project Cash Flows After Reinvestment
Reinvestment rate
10%
Initial investment
$170,000
Year
Operating cash inflows
1
2
3
NPV@10%
IRR
$0
0
248,720
和上頁相同
$16,867
13.5%
15%
$0
0
258,496
$24,213 和上頁相同
15.0%
248,720
 170,000  16,867
258,496
(1.1)3
NPV 
 170,000  24,213
3
(
1
.
1
)
248,720
-170,000 +52,000 +78,000 +100,000 IRR : (1  r )3  170,000  r  13.5% 258,496
 170,000  r  15%
3
(
1

r
)
0
1
2
3
NPV 
248,720
基本上：greater the difference between the magnitude and timing of
cash inflows, the greater the likelihood of conflicting
rankings between NPV and IRR.
理論上：用NPV，不要用IRR。因為(1)NPV假設intermediate cash
flows are reinvested at cost of capital，IRR則假設
intermediate cash flows are reinvested at IRR。NPV法的假
設較為合理且保守。(2)non-conventional cash flow常會有多
重或零個IRR的解
實務上：業界仍偏好IRR
Table 9.9
Discount rate
Low
High
Preferences Associated with Extream
Discount Rates and Dissimialr Cash
Inflow Patterns
若期初投資一樣的話
Cash inflow Pattern
Lower early year cash Higher early year cash
inflows
inflows
Preferred
Not preferred
Not preferred
Preferred
WHY?因為晚期的Cash flow會
被高折現率severely penalized
in present value terms.